Method and device for tuning and control

ABSTRACT

A method and a device for tuning and control of industrial processes having varying material flow rate. An adder is configured to add excitation signals to the controller output signal. A measurement system is configured to measure a property in response to the excitation signals. A model based tuning unit is adapted to estimate the value of at least one parameter with unknown value of a process model structure describing the effect of varying material flow rate, based on the measurements of the property and the output signal from the controller, and to calculate a model that describes the dynamics from controller output to controller input based on the estimated value of the parameter, and to perform model based tuning of the controller based on the model that describes the dynamics from controller output to controller input.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application claims priority to Swedish patent application 0502956-6filed 30 Dec. 2005 and Swedish patent application 0600321-4 filed 7 Feb.2006 is the national phase under 35 U.S.C. §371 of PCT/SE2006/050591filed 18 Dec. 2006.

TECHNICAL FIELD

This invention relates to a method and a device for tuning and controlof industrial processes having at least one actuator for affecting thequality of the produced products, and where the production speed or thematerial flow rate varies and thereby creates varying conditions for thecontrol. The invention is preferably aimed for autotuning and adaptivecontrol in rolling mill applications, e.g. for improving the flatnessfor rolled products using any number of mechanical or other actuators.The invention is also applicable to other processes where the varyingmaterial is, for example, a sheet, band, web, or a fluid.

BACKGROUND OF THE INVENTION

The flatness of a rolled product, e.g. a strip, is determined by theroll gap profile between the work rolls of a rolling mill and thethickness profile of the rolled strip. The strip flatness may then beinfluenced by manipulation of different control devices that affects themill and its work roll gap profile. Such actuators may be mechanicaldevices such as work roll bending devices, intermediate roll bendingdevices, skewing or tilting devices, intermediate roll shifting devices,top crown actuators, or thermal devices such as work rollcooling/warming actuators etc.

In flatness control for cold rolling of metals, a number of actuatorsare used that influence the flatness profile. In the standard solution,the flatness deviations are mapped to the space of actuators with thehelp of a mill matrix, which describes the static flatness response fromthe respective actuators. This decomposition leaves a number of controlloops, one for each actuator. These loops are equipped with PIcontrollers. Today, tuning of these controllers are based on off-lineidentification of models for each loop. In addition, known variations inthe model, due to varying rolling speed for example, are taken intoaccount in a parameter scheduling fashion. Two factors that make theprocess gain for each loop uncertain are its dependence on the rolledmaterial, and possible discrepancy between the assumed mill matrix andthe real behavior of the mill.

When rolling a strip, it is important to maintain the desired flatnessprofile at all times. Deviation from the desired flatness may result incostly strip breaks and scrap of produced coils. The task of theflatness control system is thus to drive the actual flatness profile asclose as possible to the desired flatness profile, which put highrequirements on the control system, in terms of calculation speed andaccuracy.

Controllers for industrial processes need to be well tuned in order toreduce quality variations and keep the produced quality withinspecifications, in spite of varying conditions. In particular, a desirefor a high production rate will often challenge the ability to controlthe process well enough to avoid both the production of off-specmaterial and interruptions in the production due to breakage. Sheetbreakages in a paper machine or band rupture in a steel rolling mill areexamples that may cause costly production losses.

The tuning of a controller is often based on a procedure to find asimple model from experiment data (from e.g. a step test) combined witha method to automatically find a good controller tuning, assuming thismodel to represent the behavior of the process well enough. For thisprocedure to be successful, it is essential that the model formulationis able to capture the actual behavior of the process during theexperiment, and that the obtained model remains valid during the normaloperation of the process with the varying conditions that may occur. Thetuning method may allow some variation around the assumed nominalbehavior, by putting a suitable degree of focus on robustness. If thereare essential variations in process dynamics—for example with varyingproduction speed—known such variations should be handled via parameterscheduling. If the variations occur during the tuning experiment, themodel identification will be seriously disturbed if standard methods areapplied.

A common approach is black-box identification that is to estimate theparameters in a discrete time formulation of the model, expressed forthe same sampling period as used in the actual control. However, in thecases where some process dynamics vary with the production speed, theestimation will be disturbed by speed variations, since the trueparameter values of the model will vary. This holds both if sampling ismade per time unit, which is the most common case, since then the partsof the dynamics that do vary with speed will give varying discrete timemodel parameters, and if sampling is done per amount of material flow,which sometimes is done for practical reasons and also gives constantdiscrete time model parameter values for dynamics which have timecharacteristics proportional to the inverse of the speed, since then theparts of the dynamics that do not vary with production speed will givevarying discrete time model parameters.

For the tuning of the PI control loops, in the standard solution forflatness control, varying rolling speed prevents use of black-boxidentification methods to determine a model. Sampling is performed perlength unit. So the model of transport behavior would be invariant forsampled data, but the actuator dynamics does not get an invariant modelfor data sampled this way, and therefore the whole discrete time modelwill vary. In addition, the sampling period may vary due to a varyingdown-sampling multiple, and varying pre-filtering in relation to this,as well.

To obtain accurate control, the controllers should be well tuned, basedon how the process responds to changes of manipulated variables. Thegain of the rolling process depends on a number of parameters that arenot well known. For flatness control, the relevant gains are influencedby what material is being rolled, the actual agreement of the assumedmill matrix with reality, and other things.

After separation of the original control task, i.e. maintained flatnessacross the width of the produced material using several actuators, intoseveral actuator-measurement loops, the current control strategy isbased on standard control loop tuning during commissioning. Normallythis is done as a single estimation of model parameters off-line foreach loop and tuning for that model. To make this activity moreefficient, the relevant model parameters should be estimated on-line andpresented to the user in real time for decision when to end theactivity. Further, the estimation should be performed in a way that isnot disturbed by speed variations.

One problem is that if the process or the material changes, the controlmay become inaccurate, even if it has been accurate previously, whichleads to poor product quality or to scrap. The change in material may,for example, cause changes in properties such as thickness, width, orhardness of the material. After a change of material, the control has tobe adapted to the properties of the new material. The faster the controlis adapted to the new properties, the faster the quality of theproduction is restored.

To avoid that problem adaptive control could be applied. Adaptivecontrol usually applies black-box models. However, discrete time modelswith varying sampling period due to varying speed will have varyingparameter values, due to the time invariant actuator associateddynamics. Thus adaptive control based on black-box identification ofsuch models will be useless.

A problem in connection with tuning controllers for industrial processeswith varying material flow rate, such as flatness measurement duringrolling, is that the sampling rate of the measuring of the controlledproperty is dependent on the flow rate, such as the rolling speed, whichleads to varying sampling intervals. It is easy and known to estimate aparameter for a time discrete model. However, it is not possible to usea time discrete model for tuning controllers for processes with varyingmaterial flow rate due to the variable sampling intervals.

SUMMARY OF THE INVENTION

The object of the present invention is to solve the problems related totuning controllers for industrial processes with varying material flowrate that causes varying control conditions.

According to one aspect of the invention, this object is achieved by amethod.

Such a method comprises:

-   -   injecting excitation signals added to the controller output        signal,    -   receiving measurements of a property of the process in response        to said excitation signals,    -   choosing a process model structure comprising at least one        parameter with unknown value, this model structure describing        the effect of varying material flow rate,    -   estimating the value of the parameter, based on the measurements        of the property and an output signal from the controller,    -   calculating a model that describes the dynamics from controller        output to controller input based on the estimated value of the        parameter, and on the basis thereof performing model based        tuning of the controller.

The present invention makes use of prior knowledge and known data of theindustrial process. According to the invention, a model structuredescribing the effect of the varying material flow rate is used. Some ofthe parameters of the model are already known. The remaining parameters,those that are unknown or are expected to vary, typically the processgain, are determined on-line by identification. This combined with atuning rule, like a lambda-tuning rule, forms a tuning method. Whenapplied to the control on-line, this forms adaptive control that takescare of process and material uncertainties and changes. When applied toautotuning, it gives a quick and reliable way to tune the controller.The present invention allows control of any type of actuator.

By using a continuous time model formulation and taking into accountwhat is known about the process, the model structure is chosen to makethe unknown parameters independent of the material flow rate, and ofother varying parameters. By independent is meant that the true valuesremain reasonably constant in spite of varying material flow rate orvarying other parameters. Thereby the number of parameters that need tobe determined by estimation is minimized, and as a consequence theestimates become more reliable. A model based tuning method is thenapplied to the total model determined from estimated parameters, knownparameters and relations and whatever signal processing actuallyapplied.

The method of the invention creates an improved, stable and robustcontrol system. The quality control problems, related to varyingconditions due to varying material flow rate with present solutions,especially in combination with varying material parameters and slowlychanging process parameters, are heavily reduced with the proposedinvention.

The method achieves the advantage over an adaptive controller based ondiscrete time black box model identification that the parameters it hasto find by estimation remain constant over longer periods, for exampleindependent of production speed, which makes the mere application ofadaptation much more feasible. This in turn provides the basis foractually being able to increase the control performance compared withnon-adaptive control. The profit of the increased performance istypically found in higher production speed at the same quality level,and/or higher produced quality at the same production speed, meaningless scrap or better price or both, and/or fewer production stops. Usedas support for initial tuning, the method can also shorten commissioningtimes.

An example where the invention is applicable is flatness control in coldrolling of metals. The tension profile is there measured with ameasurement roll that has sensors in four arrays. The measurement systemtakes a complete tension profile sample four times per revolution andconverts it to a flatness profile. We thus have a case of sampling peramount of material flow, or more precisely per length of rolledmaterial. The measurement can be mapped to a number of control loopsusing the assumed static response from the actuators. The actual dynamicresponse in the different control loops consists mainly of responses ofthe actuator servos or the heating or cooling responses in case ofthermal device actuators and of response associated with the transportof the band. The part related to the actuator is considered timeinvariant, and the time characteristics (dead-time, time constant)related to the transport are inversely proportional to the rollingspeed. Black box identification of discrete time models for this type ofprocesses is useless, since the result would be valid only for thatoperating point. The method of the invention, on the other hand,provides estimates that are both valid over the whole operating rangeand easy to interpret by the user.

Furthermore the invention will enable the operators to fully useautomatic mode, which may enhance the output of the mill in terms ofless scrap produced and/or higher rolling speed keeping the samequality.

According to an embodiment of the invention, the method compriseschoosing a process model structure, which is time continuous andcomprises parameters being independent of varying material flow rate.This embodiment makes it possible to estimate parameters for the modeldespite the variable sampling intervals.

According to a further aspect of the invention, the object is achievedby a computer program product directly loadable into the internal memoryof a computer or a processor, comprising software code portions forperforming the steps of the method, when the program is run on acomputer. The computer program is provided either on a computer-readablemedium or through a network, such as the Internet.

According to another aspect of the invention, the object is achieved bya computer readable medium having a program recorded thereon, when theprogram is to make a computer perform the steps of the method, and theprogram is run on the computer. According to another aspect of theinvention, this object is achieved by a device.

Such a device comprises an adder for adding excitation signals to thecontroller output signal, a measurement system for measuring saidproperty in response to said excitation signals, and a model basedtuning unit adapted to estimate the value of at least one parameter withunknown value of a process model structure describing the effect ofvarying material flow rate, based on said measurements of said propertyand the output signal from the controller, and to calculate a model thatdescribes the dynamics from controller output to controller input basedon the estimated value of said parameter, and to perform model basedtuning of the controller based on said model that describes the dynamicsfrom controller output to controller input.

BRIEF DESCRIPTION OF THE DRAWINGS

For a better understanding of the present invention, reference will bemade to the below drawings/figures.

FIG. 1 illustrates an outline of a rolling mill with one mill stand andcontrol devices, actuators, a flatness measurement device and theflatness control system.

FIG. 2 illustrates the invention schematically.

FIG. 3 illustrates principally a block diagram of adaptive flatnesscontrol.

FIG. 4 illustrates a flow chart of the different method steps in anadaptive flatness control system.

FIG. 5 illustrates in more detail the function of the method step“Update an on-line estimate of required model parameters” of FIG. 4.

FIG. 6 illustrates in a diagram the belief factor as function of theratio between prediction error and estimated standard deviation ofprediction errors.

DETAILED DESCRIPTION OF PREFERRED EMBODIMENT

The invention concerns a method for automatic controller tuning that canbe used for one-shot tuning and equally well for adaptive control. In atypical application of the invention, an industrial process has to someextent time-invariant dynamics, and to some extent timecharacteristics—such as dead-time and time constants—inverselyproportional to the production speed or material flow rate. Theparameterization may be chosen according to actual knowledge about thebehavior of the process and the influence of the production speed, sothat the true but unknown values of the estimated parameters will beconstant, independent of the speed and other varying parameters.Thereby, the estimation will not be disturbed by speed variations, andthere will be few parameters to estimate. As a consequence, moreaccurate estimates are obtained in a shorter time, and they are notdisturbed by running the process with normal production according toplanned schedules during an auto-tuning session or any duration ofadaptive control. The actual controller tuning uses a model thatcombines the previous knowledge of the process behavior, including theinfluence of the process speed, and the knowledge obtained through theestimated parameters.

The effect of whatever signal processing/transformation/mapping isperformed in the control system is also incorporated in the model usedfor the tuning. Thus, the invention provides adaptation for unknownvariations that have to be caught by estimation, in addition toparameter scheduling for known variations. The result is better control,and it is obtained faster and with better accuracy compared withpreviously known methods. This leads to less off-spec production andallows higher production speed with preserved quality.

In the example of flatness control in cold rolling of metals, it isknown that the actuator dynamics as well as any delays due tocommunication and processing are independent of the rolling speed. Thespeed may vary, and it will then influence the dead-time and/or timeconstant required describing the transport behavior. Furthermore, themeasurement system may apply a filter to the basic measurement and itmay down-sample the measurements so the actual sampling period becomesan integer multiple of the basic one. Both the filter transfer functionand the down-sampling multiple can be varied intentionally in relationto the rolling speed. These variations in speed, filter and samplingmultiple are known.

The parameters to estimate for each control loop may be chosen to be:

a time constant τ_(a) describing the actuator response,

a dead-time D₀ (the part of the total dead-time that is independent ofrolling speed),

a gain K, and

a factor ξ describing to which degree the transport behavior is a puredead-time or a time constant.

The true values of these parameters are independent of the speed and thevarying signal processing, as required. Expressed as lengths, the puretransport dead-time is the distance L_(d) from roll gap to measurementroll, and the pure time constant, for transport response, is the lengthL_(m) from roll gap to coiler. These distances could, in order toexpress them in time, simply be divided by the speed. The distances areconstant and known.

Since the transport response for different actuators differs and is notknown in advance, it is assumed for each individual actuator to be apure dead-time to degree ξ, and a pure time constant to degree (1−ξ).This defines the transport behavior parameter ξ. The speed independentdead-time, D₀, represents the total pure delay from measurement toactual start of change at the roll gap due to actuator movement, i.e.the average sum of processing time, communication and processing delayand any pure delays in the actuator system.

Once these parameters (K, τ_(a), D₀, ξ) have been determined, accordingto the invention, by estimation in an autotuning session duringcommissioning or re-tuning, they are all expected to remain constant,with the exception of the gain, K. Since the gain will vary with varyingmaterial, and also with possible deviation of the assumed mill matrixfrom the true one, adaptive control is applied, where the gain is theonly parameter to estimate, while at the same time known parametervariations are taken care of in a parameter scheduling fashion.

As mentioned above, adaptive flatness control according to the inventionmakes use of prior knowledge of the models, per loop, and determinestheir gains on-line by recursive identification. This combined with alambda-tuning rule (or some other tuning rule) forms adaptive controlfor each loop, applied during the initial rolling of each new coil. Themodel structure, the actuator dynamics, the speed dependent transportbehavior, and the speed independent dead-time are used as priorknowledge for the adaptive control.

The parameters included there (τ_(a), D₀, ξ) are preferably determinedin a recursive identification experiment, performed once for all foreach loop, with excitation signals supplied to the actuators in openloop or added to the controller outputs in closed loop. Known factorsinvolved in the transport behavior are the rolling speed and thephysical distances in the mill. Other factors taken into account, asprior knowledge in the tuning, are the sampling rates and the filteringapplied. These may vary also during the rolling of a single coil. Thesampling period is a multiple of the one used in the basic measurementsampling. This multiple may vary, and the basic sampling period isinversely proportional to the rolling speed. A moving average filter isapplied, the length of which may vary. It is applied at the basicsampling rate.

The recursive identification for initial determination of parametervalues, and the one used during adaptive control are quite similar,apart from the number of parameters they handle as free to estimate.They do use the knowledge of the model structure and the varyingsampling and filtering, and estimate the parameters in a continuous timeformulation of the model. Thereby, the estimated parameters areindependent of the actually used speed, sampling and filtering. Forcertain situations, the recursive identification is also supplied withseveral robustifying enhancements—compared with the standard textbookmethods—such as outlier protection, adaptation dead zones, andconstraints for estimated parameter values.

FIGS. 1-4 illustrate the invention by showing how it can be applied forflatness control. What is shown in FIG. 2 is generic.

As disclosed in FIG. 1, a flatness control system 1 is integrated in asystem comprising a mill stand 2 having several actuators 3 and rolls 4.An uncoiler, not shown, feeds a strip 5 to and through the mill stand 2,whereby the strip 5 passes a flatness measurement system 6 for example a“Stressometer” system, and is rolled up on a coiler 7. The mill stand 2may control skewing, bending and/or shifting of the rolls 4. Thereby,they change the shape of the roll gap, which is where the strip 5 isaffected as it passes between the rolls 4. There may also be heating orcooling actuators or any other type of actuators that influence the rollgap. The resulting product of the rolling process is a rolled strip 5with desired flatness. In a tandem mill, not shown, the incoming stripwould come from a preceding mill stand, instead of an uncoiler. Suchvariations between mills are unimportant from the flatness control pointof view, and the flatness control system would be identical. Theflatness control system 1 is designed comprising a number of advancedbuilding blocks, as can be seen in FIG. 3, having all requiredfunctionalities.

As disclosed in FIG. 2, illustrating principally a flow chart of theinvention, the method according to the invention involves selection of amodel structure. The further steps of the invention are performed ineither of two modes, tuning session 8 or adaptive control 9. In bothcases, excitation can be applied to the process and parameter estimationprovides values for the otherwise unknown parameters, based on data fromoperation of the process. With the model structure given, previouslyunknown parameters determined by estimation and known parameters andrelations inserted, the process model is designed. Then, if there is anysignal processing performed, the effect of it is also added to form acomplete model. This complete model is used for the controller tuning,where any adequate model based method can be applied. The modeldetermination and the model based tuning are repeated as new databecomes available with new sampling instants.

During a tuning session, the results of parameter estimation and tuningare presented to the user, thereby allowing judgment and decision whento end the session. The final result of the tuning session will beapplied to the controller if the user decides so. A tuning session canbe performed either in open loop, or with the controller in closed loopoperation. During adaptive control, the controller operates in closedloop, and tuning results are applied to the controller as they occur.Whether the control shall be active or not, and whether it shall beadaptive, is determined by programmed conditions and/or operatordecisions.

In FIG. 3, an adaptive flatness control system, based on the inventedtuning method, is disclosed. The block Controller 10 can be interpretedas either a multivariable controller or a number of single loopcontrollers. The latter case is described here, assuming the controltask to be divided into a number of control loops equal to the number ofmill actuators, each control loop with its ownsingle-input-single-output controller.

The controller outputs u(t) are fed to the actuators 3 or the actuatorservos, not shown. The actuator movements affect the roll gap in themill stand 2 and thereby the local properties p(t) of the strip justpassing the roll gap. The measurement system 6 senses the tensiondistribution s(t) across the strip 5 via the measurement roll 11 at aposition between the roll gap and the coiler 7. With a Stressometersystem, s(t) is sampled four times per revolution of the measurementroll. The flatness measurement system 6 translates the raw measurementinto a flatness profile z(t). This may involve filtering andre-sampling. The vector z(t) typically has a dimension between 16 and64. The vector z(t) is compared with the flatness reference r(t) inorder to produce a difference value, the flatness error e(t). Thisflatness error e(t) is mapped to the space of actuators to produce theso called parameterized error e^(p)(t). The dimension of u(t) ande^(p)(t) is less or equal to the number of mill actuators 3.

The tuning involves injection of excitation signals added to thecontroller outputs and the use of gathered values of u(t) and e^(p)(t)to estimate parameters of a model of the process for each control loop.In doing this, what is previously known about the process is used, sothat only the unknown parameters need to be estimated. The estimatedvalues of the unknown parameters are then used together with what wasknown before to form a complete model that describes the whole dynamicsfrom controller output to controller input, so that it can be used totune the controller with a model based tuning rule. The excitationsignal is generated until the estimation of the parameters issufficiently accurate. This tuning gives as a result the controllerparameters to be used. The parameter estimation, the forming of acomplete model and the tuning are performed for each control loop. Theparameter estimation and tuning is performed on-line and the tuningresult is also applied on-line to provide adaptive control. It is anadvantage to have few parameters to estimate in adaptive control. It canbe as few as one parameter per control loop, the process gain. Its truevalue may differ from coil to coil, but will be the same throughout thesame coil. Therefore, adaptive control should be applied during theinitial rolling of a coil, until the gain value has been found. Afterthat, the excitation signal is cut off (set to zero), and no furtherestimation will be performed for that control loop, but the tuning rulewill still be used to provide parameter scheduling, as the model will beupdated with updated previous knowledge, such as rolling speed, filtertransfer function and sampling period.

The same block scheme applies to an auto-tuning session duringcommissioning or re-tuning, except that the controller parameters fed tothe controller will then not be continuously updated for new estimatedparameter values. Instead, the progression of the estimates will bepresented to the user to allow judgment, when to consider the resultssatisfactory and end the session and quit applying excitation signals.It is also possible, in an auto-tuning session, to have the controllerin manual mode with only the excitation signal being fed to the involvedmill actuator.

The flowchart of FIG. 4 discloses the sequence of steps that areexecuted repeatedly, for the example of a flatness control system basedon the invention. The first action, described in block 12, is to get aflatness measurement from the measurement system 6. The measurement roll11 gives in this case four measurements per revolution, and themeasurement system 6 delivers a new, possibly filtered, measurement ateither this rate or the rate down-sampled by an integer factor.

The following action 13 is to form or determine the flatness error asthe deviation from the flatness reference. The measurement is a vector,and it is subtracted from a corresponding reference vector to form theflatness error.

The third step 14 is to form or determine the parameterized error, i.e.mapped to the space of control loops. The number of control loops isless than the dimension of the measurement vector, so the error isprojected to the smaller dimension corresponding to the number ofcontrol loops, using the mill matrix, which models the strip deformationper controller output.

A fourth step 15 is to update an on-line estimate of required modelparameters. Using a continuous time model, some parts of the model andits structure can be treated as known, while a smaller number ofparameters are estimated on-line as depicted in a separate figure.

A further step 16 is to combine the parameter estimates with known partsto form a complete model. When forming this final model, all is takeninto account, i.e. estimated parameters, constant parameters treated asknown, and also parameters that may vary in a known manner, such asproduction speed, sampling period, and measurement filtering (asparameter scheduling).

Another step 17 is to apply a tuning rule to get updated controllertuning. Any appropriate model based tuning method can be applied. For PIcontrollers, lambda tuning combined with model reduction to its requiredmodel form, first order plus deadtime, can be used. Inputs to the tuningare the final model and an adjustable parameter specifying the requiredtradeoff between performance and robustness.

The seventh step 18 is to apply the control, i.e. calculate thecontroller output with the retuned controller acting on theparameterized error for this loop. The controller (e.g. a PI controller)keeps operating as any normal controller. It just gets its tuningparameters updated on the fly (gain and reset time in the case of a PIcontroller).

The method steps 15 to 18 are repeated for each control loop and themethod steps 16 and 17 can be skipped if there is no change in either ofestimated parameters for the loop or parameters used for scheduling(speed, sampling period, measurement filter).

The next step 19 is to remap from control loop space to actuator spaceif they differ. If the actuators are mapped to a lower number of controlloops, the controller outputs are also remapped to the actual number ofactuators.

The next step 20 is to feed the controller outputs to the actuators orto the actuator servo setpoints. There are normally servos for eachactuator, and in those cases the controller outputs are fed to theseservos rather than directly to the actuators.

The block scheme of FIG. 5 illustrates the essential actions or steps ofan example of implementation for recursive estimation of physicalparameters in a continuous time dynamic model according to theinvention. The process modeled has inputs that influence it and areavailable for control of it, and it has outputs. It can be part of alarger process, where this part has been selected to form a control looptogether with the controller assigned to it, one loop of possibly many.

The block scheme of FIG. 5 shows activities performed when a newmeasurement becomes available. They need not necessarily be executedevery sample, but can possibly be performed more seldom according tosome criterion. One such criterion is indicated within the scheme, anadaptation deadzone 21, meaning that when there is too littleinformation in the data, no parameter update will be performed.

Measurements 22 are obtained at sampling instants, which may occur atany sampling rate, and the changes of the process input u are associatedwith these sampling instants. Thus pairs of y and u are known in 23 fora number of instants back in time. Some of these samples of y and u aregathered in a regression vector φ(t) to be used in a discrete time modelto predict the present measurement y(t). The current model is formulatedin continuous time, and some of its parameters may be treated as known,while others are to be estimated. At time t, the previous estimate ofthese parameters is the vector θ(t−1). The complete continuous timeprocess model is formed in a step 24 assuming that these estimates arethe true values, and this model is converted to the required discretetime prediction model in a step 25, using the appropriate samplingperiod. In doing this, the effect of any measurement filter 26 is alsotaken into account.

The prediction error ε(t) is formed as the difference between the actualmeasurement and the prediction in a step 27. For the update of theestimate, the gradient ψ^(T)(t) of the prediction with respect to theestimated parameters is also needed. It can be derived analytically, orit can be obtained by numeric differentiation in a step 28. The latterapproach means that predictions are calculated for a set of models wherethe estimated parameters are perturbed a little. The difference in theprediction divided by the perturbation in the parameter is anapproximation of the required partial derivative with respect to thatparameter.

Now, with the prediction error ε(t) and the transposed predictiongradient ψ(t) derived, the rest of the parameter update could be amatter of standard recursive identification. However, two importantpractical extensions are indicated in the block scheme, outlierprotection 29 and restriction of parameter estimates 30.

The outlier protection compares the size of the present prediction errorwith what it has been statistically and calculates a factor that reducesthe effect of large errors substantially as in 29. See FIG. 6, whichpresents an example of this belief factor, f_(b). The function involveson-line estimation of the variance of the prediction errors, to comparethe present size with. In a simple case, this variance estimation isperformed just by low pass filtering the squared prediction errors.

When the intended parameter update reaches outside the allowed range forany parameter, some counteraction is required to make the estimate stayinside. This can be achieved in a number of different ways. The oneindicated here assumes that the true parameter value lies inside thespecified limits. An update pointing outside is treated, by analogy withoutliers, by scaling down the prediction error and the predictiongradient with a common factor as in step 30. The value of the factor canbe chosen to place the updated estimate exactly on the border of theallowed area, or at some fraction or distance inside. An alternativeapproach that does not require the true value of a parameter to beinside the allowed range, is to set the offending parameter estimate tothe limit and re-estimate the remaining parameters. This is efficientlydone as a Markov estimate of the remaining parameters, treating theoriginal estimate as a measurement that was disturbed by a white noisewith covariance equal to the covariance matrix P associated with therecursive estimation.

The prediction gradient ψ_(r)(t)^(T) and the prediction error ε_(r)(t),after possible reduction due to outlier detection or estimates tendingoutside the allowed area, are used to determine the direction and sizeof the parameter estimate update action 31. The estimator gain K(t)multiplies the prediction error ε_(r)(t), and this gain is determined instep 32 by the prediction gradient and the covariance matrix P at theprevious instant. In case a forgetting factor λ is used, it iscalculated asK(t)=P(t−1)ψ_(r)(t)[λ+ψ_(r)(t)^(T) P(t−1)ψ_(r)(t)]⁻¹.

In the update action 33 of the covariance matrix P, there are severalpractical aspects to consider. The one of forgetting is widely known.Whether it is implemented as uniform forgetting or directionalforgetting or relies on a Kalman filter approach or addresses a targeton the trace of P, can be a matter of taste. Related to the forgettingis also the risk of covariance wind-up. It can be counteracted byrefraining from updating at all, when there is too little information,as will be the case when applying an appropriate adaptation deadzone.The covariance matrix is normally updated in factorized form, forexample by writing it as P=LDL^(T), and updating L (lower triangularmatrix with unit diagonal) and D (diagonal matrix) rather than P itself.

The basic algorithm for recursive identification based on predictionerrors is presented below, cf. Chapter 9.5 of Söderström and Stoica,“System Identification” (Prentice Hall, 1989).ε(t)=y(t)−{circumflex over (y)}(t|t−1;{circumflex over (θ)}(t−1)){circumflex over (θ)}(t)={circumflex over (θ)}(t−1)+K(t)ε(t)K(t)=P(t)ψ(t)=P(t−1)ψ(t)[1+ψ^(T)(t)P(t−1)ψ(t)]⁻¹P(t)=P(t−1)−K(t)ψ^(T)(t)P(t−1)  (1)

The expressions for the prediction ŷ(t|t−1;{circumflex over (θ)}(t−1))and its gradient ψ^(T)(t) with respect to the parameter vector willdepend on the model formulation and on assumptions regarding thecharacter of the disturbances. For the case of identification of acontinuous time model where the present prediction and response involveequidistantly sampled data, the following approach is possible. A vectorθ_(s)({circumflex over (θ)}(t−1)) holding the corresponding discretetime prediction model parameters is calculated from the model obtainedwith the estimate {circumflex over (θ)}(t−1) using the actual samplingperiod, and the involved values of measurement samples and manipulatedvariables (those required for the prediction) are gathered in a vectorφ(t−1). Then the prediction is formed asŷ(t|t−1;{circumflex over (θ)}(t−1))=φ^(T)(t−1)θ_(s)({circumflex over(θ)}(t−1))  (2)

There is, here, an underlying assumption that the disturbances can bemodeled according to what is known as an ‘arx’ structure for thediscrete time model. (arx=Auto−Regressive with control.) An ‘arx’ modelis often written (with e(t) denoting white noise):y(t)+a ₁ y(t−1)+ . . . +a _(n) _(a) y(t−n _(a))=b ₁ u(t−k)+ . . . +b_(n) _(b) u(t−k−n _(b)+1)+e(t)  (3)

The optimal one-step-ahead predictor for this model is of the type shownabove, in (2), withφ^(T)(t−1)=[−y(t−1) . . . −y(t−n _(a))u(t−k) . . . u(t−k−n _(b)+1)]θ_(s)^(T) =[a ₁ . . . a _(n) _(a) b ₁ . . . b _(n) _(b) ]  (4)

With this approach, the steps to take in order to form the requireddiscrete time parameter vector involve forming the continuous timemodel—based on the estimated parameters and what else is known—and thentranslating it to discrete time, in a well-known manner, and expressingthe resulting model in transfer function form so that the parameters a₁. . . a_(n) _(a) b₁ . . . b_(n) _(b) and k are obtained. This isillustrated by the following example, a first order process with adeadtime that partly depends on the transport flow rate, v. Thecontinuous time model is in this example

$\begin{matrix}{\frac{K}{1 + {\tau\; s}}{\mathbb{e}}^{{- D_{0}}s}{\mathbb{e}}^{{- L}\text{/}v^{s}}} & (5)\end{matrix}$

In a real case L would probably be considered as a known parameter aswell as the flow rate or speed, v. The remaining parameters—the gain K,the time constant τ, and the speed independent part D₀ of thedeadtime—are either considered known, or constitute part of theestimated parameter vector θ, which means they are the ones that gettheir values by recursive estimation. Anyhow, the model (5) is formed.The corresponding discrete time model for the sampling period h is

$\begin{matrix}{K\;\frac{1 - \beta + {\left( {\beta - \alpha} \right)q^{- 1}}}{1 - {\alpha\; q^{- 1}}}q^{- k}} & (6)\end{matrix}$where α=e^(−h/τ), β=e^(−(kh−D)/τ), D=D₀+L/v, and k is D/h rounded to thenearest higher integer. Thus, the corresponding arx model is of the form(3), with k as given above anda ₁ =−αb ₁ =K(1−β)b ₂ =K(β−α)n _(a)=1n _(b)=2  (7)

In a general case, the continuous time model would most conveniently beformulated as a state space model, which is converted first to adiscrete time state space model, and then to transfer functionform—still in accordance with the illustrating example above. Theapproach allows any combination of known and unknown parameters in thecomplete model. If, for example, there is a filter applied to the rawmeasurements to get the sampled values available for use in theidentification, then that known filter would be accounted for in thederivation of the expressions for the parameters a₁ . . . a_(n) _(a) b₁. . . b_(n) _(b) .

The required prediction gradient ψ^(T) (t) can be derived analytically,especially for simple model structures. Alternatively, it can beobtained by numerical differentiation in the following way. A smalldeviation is introduced in each of the estimated parameters (elements ofθ), one by one, and the prediction is calculated for each case. Theresulting deviation in prediction is then divided by the parameterdeviation, for each of the estimated parameters, to form thecorresponding element of the gradient.

If discrete time model parameters were to be estimated, like a₁ . . .a_(n) _(a) b₁ . . . b_(n) _(b) of the model type (3), you can see from(6) and (7) for the first order example that variations in any of theactual parameters gain (K), time constant (τ) or speed independentdeadtime (D₀) will affect at least two of the estimated parameters a₁,b₁, and b₂. Since any variations in the true basic parameters gain (K),time constant (τ) or speed independent deadtime (D₀) are expected to beindependent from each other, and also because it is possible for anyuser to interpret the meaning of their values, estimating them directlyis better than estimating a₁, b₁, and b₂. The user will be able to judgewhether the estimated values are plausible. The calculations involved toestimate the parameters of the continuous time model are more complex,but that problem is solvable with readily available hardware today, oncethe required software implementation of the developed algorithms isdone.

The tuning of the controller is based on a model of the process. Alsothe effect of sampling, and in particular of filters applied to themeasurement are taken into account. Any model based tuning method,suitable for the model and controller types used, could be applied. ForPI control, a very simple one is known as lambda tuning, aiming at aclosed-loop system with specified time constant lambda (λ). Often theuser specifies the lambda factor, or slowdown factor, λ_(f), rather thanlambda itself. In its well-known basic form, lambda tuning is onlyapplicable to first order systems with or without deadtime. It can alsobe applied to a higher order model, after simplification of the model toorder one. As an example of a simple model order reduction, a thirdorder model with three time constants and a deadtime

$\begin{matrix}{{\frac{K\;{\mathbb{e}}^{- {Ds}}}{\left( {1 + {\tau_{1}s}} \right)\left( {1 + {\tau_{2}s}} \right)\left( {1 + {\tau_{3}s}} \right)}\mspace{14mu} T_{1}} \geq T_{2} \geq T_{3}} & (8)\end{matrix}$can, for this purpose, be approximated with the first order plusdeadtime model

$\begin{matrix}{{\frac{K\;{\mathbb{e}}^{{- D_{r}}s}}{1 + {\tau_{1}s}}\mspace{14mu} D_{r}} = {D + \frac{\tau_{2} + \tau_{3}}{2}}} & (9)\end{matrix}$

Then lambda tuning applied to this model gives the PI controller gain kand reset time T₁ as

$\begin{matrix}{{T_{I} = \tau_{1}}{k = {\frac{T_{I}}{K\left( {\lambda + D_{r} + T_{s}} \right)} = \frac{T_{I}}{K\left( {\lambda + D + \frac{\tau_{2} + \tau_{3}}{2} + T_{s}} \right)}}}} & (10)\end{matrix}$if the controller sampling period is T_(s). This summarizes one variantof lambda tuning for models with one, two or three time constants and adeadtime (τ₃ and τ₂ are allowed to be zero in the formula (10)). Thelambda λ in (10) would be determined from the lambda factor λ_(f) as

$\begin{matrix}{\lambda = {\lambda_{f}\left( {\tau_{1} + \frac{D + \tau_{2} + \tau_{3}}{2}} \right)}} & (11)\end{matrix}$

If there is a measurement filter, not included in the process model, itis taken into account by including it in the dynamic model to be reducedto first order. The case of an FIR filter (finite impulse response) withn_(f) equal coefficients, for example, can for this purpose beapproximated with a first order time constant τ_(f)=(n_(f)−1)T_(b)/2,where T_(b) is the filter sampling period.

There are other variants of the precise formulation of lambda tuning,regarding for example the inclusion of the sampling period Ts in theformula, the relation between λ and λ_(f), application to integratingprocesses, and for application to higher order models also the way ofreducing the model order. Those variants are not detailed here.Furthermore, lambda tuning is only mentioned as an example, and themethod described in the invention is equally well applicable with othervariants of model based tuning.

It is noted that while the above describes exemplifying embodiments ofthe invention, there are several variations and modifications which maybe made to the disclosed solution without departing from the scope ofthe present invention as defined in the appended claims.

1. A method for tuning a controller controlling a property of anindustrial process having varying material flow rate, the methodcomprising: injecting excitation signals added to an output signal ofthe controller, receiving measurements of said property in response tosaid excitation signals, choosing a process model structure which istime continuous and comprises at least one parameter with unknown value,the parameter being independent of varying material flow rate,estimating a value of said at least one parameter, based on saidmeasurements of said property and an output signal from the controller,calculating a model that describes dynamics from controller output tocontroller input based on the estimated value of said parameter, and ona basis thereof performing model based tuning of the controller,reducing a parameter update size, when an unrestricted update reachesoutside an area of defined allowed parameter ranges, but making aparameter update in a same direction in a parameter space, and applyinga same reduction factor to both regressors and prediction error, to beused in both parameter update and update of matrix holding informationnecessary in recursive estimation, thereby keeping parameter estimateswithin allowed ranges.
 2. The method according to claim 1, furthercomprising: choosing a process model structure comprising at most onemodel parameter per input/output pair being affected by varying actualgain of the industrial process.
 3. The method according to claim 1,further comprising: choosing a process model structure comprising atmost one model parameter per actuator being affected by varying actualresponse times of actuators.
 4. The method according to claim 1, furthercomprising: including, in the process model structure, any delays due todata processing and communication, and choosing said process modelstructure such that variations of said delays do not influence more thanone model parameter per model input.
 5. The method according to claim 1,further comprising: composing said process model structure of two parts,one part describing transport behavior where possible deadtimes andpossible time constants are inversely proportional to the material flowrate, and another part that is independent of the material flow rate. 6.The method according to claim 1, further comprising: deriving a firstorder plus deadtime model for each part of said model, introducing atransport behavior parameter that defines a degree of pure deadtime inrelation to pure first order response of the transport behavior, having,in a case of pure deadtime transport behavior, a deadtime described by aknown distance, having, in the case of pure first order transportbehavior, an associated time constant described by the known distance,and estimating at least one of the parameters gain, flow independenttime constant, flow independent deadtime and transport behaviorparameter.
 7. The method according to claim 1, further comprising:estimating at least one parameter using a prediction error method. 8.The method according to claim 7, further comprising: choosing theprocess model structure$\frac{K\;{\mathbb{e}}^{{- D_{0}}s}}{1 + {\tau\; s}}\frac{{\mathbb{e}}^{{- \frac{L_{d}}{v}}\xi\; s}}{1 + {\frac{L_{m}}{v}\left( {1 - \xi} \right)s}}$wherein K represents the estimated parameters gain, D₀ represents flowindependent deadtime, ξ represents transport behavior parameter, L_(d)represents known distance describing the deadtime, and L_(m) representsthe known distance describing the associated time constant.
 9. Themethod according to claim 1, further comprising: reducing, for a case oflarge prediction errors, an effect of measurements and regressorsaccording to a belief factor calculated from a ratio between predictionerror size and estimated standard deviation of previous predictionerrors, and thereby achieving protection against outliers.
 10. Themethod according to claim 1, further comprising: sampling processoutputs at a basic sampling rate, applying a filter with the same basicsampling rate, and re-sampling to a slower sampling rate, this ratebeing used for logging of values from operation of the industrialprocess, and including an effect of this sampling, filtering andre-sampling in prediction calculations and parameter estimate updates.11. The method according to claim 1, further comprising: performing anidentification experiment meaning operating the industrial process withintentional excitation influencing at least one manipulated variable,and estimating at least one parameter on-line during said identificationexperiment.
 12. The method according to claim 11, further comprising:presenting results to a user in real-time, thereby allowing userdecision to end the identification experiment.
 13. The method accordingto claim 11, further comprising: estimating fewer parameters duringoperation with on-line updating of the controller than during theidentification experiment, and allowing an parameter estimation resultfrom the identification experiment to define the value of at least oneparameter, and treating this parameter or these parameters as knownduring the operation with on-line updating of the controller.
 14. Themethod according to claim 1, further comprising: calculating on-linesaid model based tuning of the controller.
 15. The method according toclaim 1, further comprising: estimating at least one parameter on-lineduring operation of the industrial process and while controlling it withsaid controller, performing on-line said model based tuning calculationsfor the controller, and applying the tuning result to said controlleron-line, thereby achieving true adaptive control.
 16. The methodaccording to claim 1, further comprising: using lambda tuning as modelbased tuning method for said controller.
 17. A device for tuning acontroller controlling a property of an industrial process havingvarying material flow rate, the device comprising: an adder for addingexcitation signals to a controller output signal, a measurement systemfor measuring said property in response to said excitation signals, anda model based tuning unit adapted to estimate a value of at least oneparameter with unknown value of a time continuous process modelstructure describing an effect of varying material flow rate, based onsaid measurements of said property and the controller output signal, theparameter being independent of the varying material flow rate, and tocalculate a model that describes dynamics from controller output tocontroller input based on the estimated value of said parameter, toreduce a parameter update size, when an unrestricted update reachesoutside an area of defined allowed parameter ranges, but making aparameter update in the same direction in a parameter space, to apply asame reduction factor to both regressors and prediction error, to beused in both parameter update and update of matrix holding informationnecessary in recursive estimation, thereby keeping parameter estimateswithin allowed ranges, and to perform model based tuning of thecontroller based on said model that describes the dynamics fromcontroller output to controller input.
 18. A non-transitory computerreadable medium storing computer readable program code for causing acomputer to perform the steps of: injecting excitation signals added toan output signal of a controller, receiving measurements of saidproperty in response to said excitation signals, choosing a processmodel structure comprising at least one parameter with unknown value,this model structure describing an effect of varying material flow rate,estimating a value of said at least one parameter, based on saidmeasurements of said property and an output signal from the controller,calculating a model that describes dynamics from controller output tocontroller input based on the estimated value of said parameter, and ona basis thereof performing model based tuning of the controller,reducing a parameter update size, when an unrestricted update reachesoutside an area of defined allowed parameter ranges, but making aparameter update in the same direction in a parameter space, andapplying a same reduction factor to both regressors and predictionerror, to be used in both parameter update and update of matrix holdinginformation necessary in recursive estimation, thereby keeping parameterestimates within allowed ranges.